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A NOTE ON ACCELERATED SEQUENTIAL ESTIMATION

OF THE MEAN OF NEF-PVF DISTRIBUTIONS

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ARUP BOSE^{ 1} AND NITIS
MUKHOPADHYAY^{ 2}

^{1} *Stat-Math Unit, Indian Statistical Institute, 203
Barrackpore
Trunk Road,*

Calcutta 700 035, India

^{2} *Department of Statistics, University of Connecticut, UBox
120,*

196 Auditorium Road, Storrs, CT 06269, U.S.A.
(Received December 20, 1993)

**Abstract.**
The minimum risk point estimation for the mean
is addressed for a natural exponential family (NEF) that also has a
power variance function (PVF) under a loss function given by the
squared error plus linear cost. An appropriate accelerated version of
the full purely sequential methodology of Bose and Boukai
(1993*b*, submitted) is proposed along the lines of
Mukhopadhyay (1993*a*, Tech. Report, No.93-27,
Department of Statistics, University of Connecticut) in order to
achieve operational savings. The main result provides the asymptotic
second-order expansion of the regret function associated with the
accelerated sequential estimator of the population mean.

*Key words and phrases*:
Natural exponential family,
power variance function, mean estimation, minimum risk,
acceleration, regret expansion, operational savings.

**Source**
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